The creature standing rather unsteadily in a zoology museum in London is among the rarest in the world, and frankly she’s not looking her best.

The quagga in the Grant Museum, part of University College London, is one of only seven remaining quagga skeletons anywhere, a cousin of the zebra which became extinct in 1883. The museum itself is a rare survivor, the last of what were once many university zoology museums in the capital.

Quaggas looked like zebras which had forgotten to put on their pyjama trousers, half stripey, half plain brown. Once plentiful on the South African plains, quaggas were hunted both for their unusual skins and by stock keepers to reduce competition for food. London Zoo once had one, but it was only realised that the animal was extinct when the quagga in Amsterdam died on 12 August 1883. The zoo sent out hunters to bring back a new one and found there were none.

The bones came into the Grant collection in the late 19th century, and the skeleton was mounted – the only mounted specimen in the UK – by museum technicians in 1911, but not very well. The bones were bolted onto a hand-forged iron frame, in some places by driving screws straight through fragile bones. Something unpleasantly treacle-like has oozed out around the breast bones.

Even the most eagle-eyed visitors rarely spot that all the bones of the neck were actually mounted upside down, but many do notice that she only has three legs: the museum in the Rockefeller Building in University Street is still a teaching collection, and at some point the missing leg was loaned and never returned.

In 1911 the quagga was a cheap and quick job: she was mounted with five other large skeletons for a total cost of £14.

“To be fair to them, they had no idea they were dealing with such a rarity,” Ashby said. “She came into the collection as a zebra. It’s one of the Grant’s more embarrassing stories, actually. We used to have two zebras, now we have none.”

It was only in 1972 that experts took a really close look at the zebras. One turned out to be a donkey, now leaning rather forlornly against the balcony railings and in need of restoration work himself, and the other was revealed as the quagga.

The museum’s scientists take a dim view of a controversial selective breeding project in South Africa to recreate an animal which looks like a quagga, but have launched the Bone Idol fundraising appeal to restore their own specimen, along with 38 other historic skeletons in the collection, including the spectacular skull and antlers of another extinct animal, the giant Irish deer, which a group of academics bought straight off a pub wall in Ireland.

The largest skeleton in the museum, a (hornless) greater Indian one-horned rhino that was part of the 1911 batch, has already been removed from display for conservation work and the quagga is next on the list. Her bones will be carefully dismantled, cleaned – the old technique of rotting off the meat by steeping skeletons in a giant tank in the university attics is no longer favoured, much to the relief of staff – and remounted on an anatomically correct support that should preserve her forever. Meanwhile, the search for her fourth leg goes on.

• The Grant Museum of Zoology, UCL, London, is open free to the public, Monday-Saturday 1-5pm